Numerical Approaches of Pricing European Options in the Cox-Ross-Rubinstein Models

Abstract

The Cox-Ross-Rubinstein (CRR) market model is one of the simplest and easiest ways to analyze the option pricing model. CRR has been employed to evaluate a European Option Pricing (call options) model without complex elements, including dividends, stocks, and stock indexes. Instead, it considers only a continuous dividend yield, futures, and currency options. The CRR model is simple but strong enough to describe the general economic intuition behind option pricing and its principal techniques. Also, it gives us basic ideas on how to develop financial products based on current deviations and volatilities. The paper investigates the CRR model using numerical approaches with python code. It provides a practical event using the mathematical model to demonstrate the application of the model in the financial market. First, the paper provides a simple example to figure out the basic concept of the model. Only a two-period binomial model based on the introductory definitions of the call options makes us understand the concept more easily and quickly. Next, we used actual data on Tesla stock fluctuations from the Nasdaq website (See section 3). We developed the python code to make it easier to understand figures, including tables and graphs. The code allows us to visualize and simplify the model and output data. The code analyzes the stock data to evaluate the probability of the stock’s price increasing or decreasing. Then, it used the CRR model to estimate all possible cases for the stock’s prices and investigate the call and put option pricing. The code was based on the introductory code of binomial option pricing, but we improved it to get more information and provide more detailed results from the data. The detailed codes are provided in section 3 of the paper. As a result, we believe the CRR model is a fundamental formula, but the improved python code can suggest a new direction for evaluating the probability and investigating the value of the stocks. Also, we expect to develop the code to extend the Black Scholes Pricing model, increasing the number of periods.